A metal sphere of radius R and specific heat C is rotated about an axis passing through its centre at a speed n rotation/second. It is suddenly stopped and 50% of its energy is used in increasing its temperature, then choose the correct statement(s) from the following?

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Kinetic energy used to raise the temperature of the sphere is 2π2n25MR2

Kinetic energy used to raise the temperature of the sphere is 5π2n3MR

The rise in the temperature of the sphere is 4π2n2R27C

The rise in the temperature of the sphere is 2π2n2R25C

answer is A.

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Detailed Solution

Kinetic energy of the sphere K=12Iω2=12×25MR2(2πn)2=45π2n2MR2Kinetic energy used to raise, the temperature =0.545π2n2MR2=25π2n2MR2∴ΔT=2π2n2R25C

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